Random matrices and log-gases
Random matrices appear naturally in the modelling of systems where (i) a large number of interacting agents are involved and (ii) a detailed knowledge of the connections’ properties is lacking. In such cases a reasonable first order approximation is to assume that the connections’ matrix is a random matrix given by a suitable law.
The eigenvalues of certain random matrices have been shown to be distributed as particles interacting with logarithmic repulsion under an external confining potential. We use this analogy in order to better understand the properties of random matrices and their spectra.

Neuronal networks
Characterizing the influence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences.
I focus on the study of the dynamics of agents interacting on weighted disordered networks with strong correlations in the connectivity. In particular I consider the case where the connectivity matrix is the sum of a deterministic (structure) part plus a random (disorder) part. In order to understand such systems I principally use results from random matrix theory and dynamical systems together with intensive numerical simulations.